Thread: slope of the tangent line

Let f(x) = 1/x-3. Calculate the difference quotient F(0+h)-f(0)/h for

h =.1 = (-.114942587)
h =.01 = (-.1114827202)
h = -.01 = (-.1107419712)
h = -.1 = (-.1075268817)
I understood how to get these values but then it asked:
If the slope of the tangent line to the graph of F(x) at x = 0 was -1/n^2 for some integer n, what would you expect n to be?
n = ?
This is the part I do not understand, could someone please explain this to me.
Thank You,
Keith Stevens

Originally Posted by kcsteven

Let f(x) = 1/x-3. Calculate the difference quotient F(0+h)-f(0)/h for

h =.1 = (-.114942587)
h =.01 = (-.1114827202)
h = -.01 = (-.1107419712)
h = -.1 = (-.1075268817)
I understood how to get these values but then it asked:
If the slope of the tangent line to the graph of F(x) at x = 0 was -1/n^2 for some integer n, what would you expect n to be?
n = ?
This is the part I do not understand, could someone please explain this to me.
Thank You,
Keith Stevens

i didnt check this, but you got the answers to be roughly -0.1 right. so we want n so that -1/n^2 = -0.1. so idealy we want n^2 = 10. since -1/10 = -0.1. but that would mean n = sqrt(10) which is not an integer. so the closest we can get is say, n^2 = 9. so -1/n^2 = -1/9 = -0.111111111... so then n=3

Originally Posted by kcsteven

Let f(x) = 1/x-3. Calculate the difference quotient F(0+h)-f(0)/h for

h =.1 = (-.114942587)
h =.01 = (-.1114827202)
h = -.01 = (-.1107419712)
h = -.1 = (-.1075268817)
I understood how to get these values but then it asked:
If the slope of the tangent line to the graph of F(x) at x = 0 was -1/n^2 for some integer n, what would you expect n to be?
n = ?
This is the part I do not understand, could someone please explain this to me.
Thank You,
Keith Stevens

Hi Keith it's Andrew. Jhevon was right but I posted some steps that might give you more of a visual perspective.

Click on the following two links:

a. http://item.slide.com/r/1/131/i/ohC2...s5OHgEjT9ZCth/
b. http://item.slide.com/r/1/66/i/hRo6v...aqPDkV55xVeZk/

Also Keith don't forget to check Dr. W's website out either. We have a calculator lab due on March 21.

Pet Peeve alert!! Warning! Danger, Will Robinson! Warning! Warning!

I know what you were TRYING to say, but how can the following be true statements?

Originally Posted by kcsteven

h =.1 = (-.114942587)
h =.01 = (-.1114827202)
h = -.01 = (-.1107419712)
h = -.1 = (-.1075268817)

Just a suggestion to be careful about what you are writing. Professors have taken points on exams for even less serious errors. My suggestion is to be careful about what you write at all times.

-Dan